Question

Identify the oblique asymptote of f(x) = quantity 2 x squared plus 3 x plus 8 over quantity x plus 3.

Answer 1

The answer is y=2x - 3

Answer 2

The oblique asymptote in the slope-intercept form is:
y = m x + b, where:
m =
`\lim_(x \to \infty) ( 2x^(2)+3x+8)/( x^(2) +3x)` = 2
b =
`\lim_(x \to \infty) ( x^(2) +3x+8)/(x+3) - 2 x = \\ \lim_(x \to \infty) (2 x^(2) + 3 x + 8 - 2 x^(2) -6x)/(x+3)= \\ \lim_(x \to \infty) (-3x+8)/(x+3)` = -3
Answer: y = 2 x - 3